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<b>set </b><font color="Maroon">N</font> =  <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ;<br/>
<a NAME="E1:124"/>
(  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ,the <a href="group_1.html#U1">mult</a> of <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a>  #) <a href="hidden.html#R1">=</a>  <a href="monoid_0.html#K8" target="_self">&lt;NAT,*&gt;</a>  &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>( <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a> ) )
 
<b>by </b><i>, <a class="ref" href="monoid_0.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:124"/>
 <a href="monoid_0.html#K9" target="_self">&lt;NAT,*,1&gt;</a>  <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="binop_2.html#K48">multnat</a> ,1 #)
 <b>by </b><i>, <a class="txt" href="monoid_0.html#E27"><i><font color="Green">Lemma57</font></i></a></i>;<br/>


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